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874

Appendix II.

where the exponent n represents the number of cords; and the
real advantage is thus shewn. The assumption, however, that
pulley friction and rope-bending resistance vary similarly is not
quite true, the latter increasing more rapidly than the former.
Comparing with experiment,

P- W
i : i block;    m =    -    =   -195    at max. effy

U1    ,      W
2 : i block ;     =
'    P

m

= i*54

which, by experiment =1-52      at max. effy.

i

r\i

= 2*62

W
4 : i block;    ~

i -

m

which, by experiment = 2*25      at max. effy.
In the case of a screw jack, the P : W line passed through the

\

t r*

'

Fuj. 635.

origin, P & W vanishing simultaneously, because the screw was
reckoned as load. The efficiency was therefore constant at all
loads, being -3535 with a screw 1-92" mean diameter and pitch
", the velocity ratio being 59-33 : i. The lever was repre-
sented by a pulley mounted on the screw axis. Here again the
efficiency can be found by calculation. Let F G, Fig. 835, be the
mean screw circumference, and H G the pitch, the nut being
moved by force P. Neglecting friction, there are three balancing
forces, P, R, and W; and the force diagram is A B c.

W
F

A B
B C

circumference

pitch

i

tanO